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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<i><font color="Green">E36</font></i>:  <a href="complex1.html#K3" target="_self">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T19" target="_self">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K3" target="_self">Re</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> 0
<b>by </b><i><a class="ref" href="complex1.html#T25" target="_self">Th25</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="complex1.html#D2" target="_self">Def2</a></i>
;<br/>
 <a href="complex1.html#K4" target="_self">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T19" target="_self">Th19</a></i>
<br/>.= 
0 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K4" target="_self">Im</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#D3" target="_self">Def3</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="complex1.html#T26" target="_self">Th26</a></i>
;<br/>
<b>hence </b><a NAME="E3:36"/>
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7" target="_self">&lt;i&gt;</a> </span>)</span>
 <b>by </b><i><a class="txt" href="complex1.html#E1:36"><i><font color="Green">E36</font></i></a>, <a class="txt" href="complex1.html#E13"><i><font color="Green">Lemma9</font></i></a></i>;<br/>


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